Type 1.
Annuluses formed by an infinite family of concentric circles
in geometric progression with common ratio r (0 < r < 1).
Equations of the circles:
x² + y² = (1 + r + r² + r³ + ... + r^k)², k=0,1,2,3,....
Regions determined by inequalities formed by five infinite families
of concentric annuluses.
r = 1 / golden ratio = 2 / (1+√5) ~ 0.618
h = 2 (h is the displacement parameter.)
r = 0.75, h = 2.5
r = 0.8, h = -3
r = 1 / golden ratio, h = 1.5
r = 0.75, h = 2.5
Type 2.
Annuluses formed by an infinite family of concentric circles
in geometric progression with common ratio r (0 < r < 1).
Equations of the circles:
x² + y² = (r^k)², k=0,1,2,3,....
r = 0.5, h = 0.25
r = 0.8, h = 0.5
r = 0.999, h = 1
r = 0.8, h = 0.5
Type 3.
Annuluses formed by two infinite families of concentric circles.
r1 = the common ratio of the outer family (0 < r1 < 1)
r2 = the common ratio of the inner family (0 < r2 < 1)
r1 = r2 = 0.5, h = 1.5
r1 = 0.65, r2 = 0.8, h = 2.5
r1 = 1 / golden ratio, r2 = 0.75, h = 2
r1 = r2 = 0.5, h = 1.5
( Mathematical software used: Graph )
Related posts:
- Infinite Families of Concentric Circles (2)
- Infinite Families of Tangent Circles (1)
- Infinite Families of Tangent Circles (2)
- Infinite Families of Tangent Circles (3)
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